The method of generating functions for the calculation of matrix elements in the deformed-harmonic oscillator basis

✍ Scribed by Rainer W Hasse

• Publisher: Elsevier Science
• Year: 1973
• Tongue: English
• Weight: 996 KB
• Volume: 80
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(73)90321-7

✦ Synopsis

The method of generating functions which was previously only employed for the spherical basis of harmonic-oscillator single-particle wave functions is here generalized to the deformed (=cylindrical = asymptotic) basis. One-center and two-center matrix elements which are important in fission or heavy-ion scattering theories are obtained for various operators and potentials, i.e., spin-orbit, Z-squared, Gaussian, or Gaussian multiplied by a polynomial, etc. If they cannot be calculated explicitely, recurrence formulae are evaluated. The method circumvents integrating the matrix elements by the introduction of generating parameters and looking for the coefficient of some power of the generating parameter in the expansion of the generating function. The method is further simplified by transforming the operators acting on the wave functions into operators which act onto the generating function or into functions to be multiplied by the generating integral.